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s11_mthsc208_hw01

# s11_mthsc208_hw01 - MthSc 208 Spring 2011(Differential...

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MthSc 208, Spring 2011 (Differential Equations) Dr. Macauley HW 1 Due Friday January 21st, 2010 (1) Let P ( t ) be the net worth of an investment after t years, that is growing at a 5% rate. Suppose that after two years, the investment is worth \$200. Write down an initial value problem (the differential equation & initial condition) for P , and sketch its solution. (2) Let T ( t ) be the temperature of a cup of water t minutes after being placed in a room where the ambient temperature is 72 . (a) Write down a differential equation that T satisfies. (b) Sketch the solution curve of the solution satisfying T (0) = 100. (c) Sketch the solution curve of the solution satisfying T (0) = 40. (d) Sketch the solution curve of the solution satisfying T (0) = 72. (3) Repeat the previous exercise, except let T ( t ) be the temperature of a sheet of metal (which cools down and heats up much quicker than water). Qualitatively, what is the difference between the solution curves in these two problems? Which value of k is bigger and why?
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